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Concept

Théorème fondamental de l'arithmétique

Publications associées (18)

Energy Efficient Logic and Memory Design With Beyond-CMOS Magnetoelectric Spin-Orbit (MESO) Technology Toward Ultralow Supply Voltage

Kyojin Choo

Devices based on the spin as the fundamental computing unit provide a promising beyond-complementary metal-oxide-semiconductor (CMOS) device option, thanks to their energy efficiency and compatibility with CMOS. One such option is a magnetoelectric spin-or ...

Ieee-Inst Electrical Electronics Engineers Inc2023

The double exponential runtime is tight for 2-stage stochastic ILPs

Kim-Manuel Klein, Alexandra Anna Lassota

We consider fundamental algorithmic number theoretic problems and their relation to a class of block structured Integer Linear Programs (ILPs) called 2-stage stochastic. A 2-stage stochastic ILP is an integer program of the form min{c(T)x vertical bar Ax = ...

SPRINGER HEIDELBERG2022

Hopf algebras and Hopf-Galois extensions in infinity-categories

Aras Ergus

In this thesis, we study interactions between algebraic and coalgebraic structures in infinity-categories (more precisely, in the quasicategorical model of (infinity, 1)-categories). We define a notion of a Hopf algebra H in an E-2-monoidal infinity-catego ...

EPFL2022

Strictly Real Fundamental Theorem Of Algebra Using Polynomial Interlacing

Soham Basu

Without resorting to complex numbers or any advanced topological arguments, we show that any real polynomial of degree greater than two always has a real quadratic polynomial factor, which is equivalent to the fundamental theorem of algebra. The proof uses ...

CAMBRIDGE UNIV PRESS2021

Individual differences in the perception of visual illusions are stable across eyes, time, and measurement methods

Michael Herzog, Lukasz Grzeczkowski, Aline Françoise Cretenoud

Vision scientists have tried to classify illusions for more than a century. For example, some studies suggested that there is a unique common factor for all visual illusions. Other studies proposed that there are several subclasses of illusions, such as il ...

Association for Research in Vision and Ophthalmology2021

Linear Flavour-Wave Theory of SU(N) Lattice Models with Arbitrary Irreducible Representations

Francisco Hyunkyu Kim

This thesis explores various approaches of studying the long-range colour order of antiferromagnetic SU(N) Heisenberg models with the linear flavour-wave theory (LFWT). The LFWT is an extension of the well-known SU(2) spin-wave theory to SU(N), and this se ...

EPFL2019

On the fundamental domain of affine Springer fibers

Zongbin Chen

Let G be a connected reductive algebraic group over an algebraically closed field k,gamma is an element of g( k(( epsilon ))) a semisimple regular element, we introduce a fundamental domain F gamma for the affine Springer fibers X gamma. We show that the p ...

Springer Heidelberg2017

On some algebraic and extremal problems in discrete geometry

Seyed Hossein Nassajianmojarrad

In the present thesis, we delve into different extremal and algebraic problems arising from combinatorial geometry. Specifically, we consider the following problems. For any integer

n\ge 3

, we define

e(n)

to be the minimum positive integer such that an ...

EPFL2017

A variational investigation of the SU(N) Heisenberg model in antisymmetric irreducible representations

Jérôme Dufour

Motivated by recent experimental progress in the context of ultra-cold multi-colour fermionic atoms in optical lattices, this thesis investigates the properties of the antiferromagnetic SU(N) Heisenberg models with fully antisymmetric irreducible represent ...

EPFL2016

Inverse Rendering of Lambertian Surfaces Using Subspace Methods

Quy Ha Nguyen, Minh Do

We propose a vector space approach for inverse rendering of a Lambertian convex object with distant light sources. In this problem, the texture of the object and arbitrary lightings are both to be recovered from multiple images of the object and its 3D mod ...

Ieee-Inst Electrical Electronics Engineers Inc2014

On the Cryptanalysis of Public-Key Cryptography

Joppe Willem Bos

Nowadays, the most popular public-key cryptosystems are based on either the integer factorization or the discrete logarithm problem. The feasibility of solving these mathematical problems in practice is studied and techniques are presented to speed-up the ...

EPFL2012

Efficient SIMD arithmetic modulo a Mersenne number

Arjen Lenstra, Joppe Willem Bos, Thorsten Kleinjung

This paper describes carry-less arithmetic operations modulo an integer 2^M − 1 in the thousand-bit range, targeted at single instruction multiple data platforms and applications where overall throughput is the main performance criterion. Using an implemen ...

IEEE Computer Soc Press2011

Decision Procedures for Program Synthesis and Verification

Ruzica Piskac

Decision procedures are widely used in software development and verification. The goal of this dissertation is to increase the scope of properties that can be verified using decision procedures. To achieve this goal, we identify three improvements over the ...

EPFL2011

Annihilating Polynomials for Quadratic Forms

Let K be a field with char(K) ≠ 2. The Witt-Grothendieck ring (K) and the Witt ring W (K) of K are both quotients of the group ring ℤ[𝓖(K)], where 𝓖(K) := K*/(K*)2 is the square class group of K. Since ℤ[𝓖(K)] is integra ...

EPFL2010

On Hermitian Pfister Forms

Let K be a field of characteristic different from 2. It is known that a quadratic Pfister form over K is hyperbolic once it is isotropic. It is also known that the dimension of an anisotropic quadratic form over K belonging to a given power of the fundamen ...

2008

Efficient multiplication using type $2$ optimal normal bases

Mohammad Amin Shokrollahi

In this paper we propose a new structure for multiplication using optimal normal bases of type

2

. The multiplier uses an efficient linear transformation to convert the normal basis representations of elements of

F_{q^{n}}

to suitable polynomials of deg ...

2007

Trace coordinates of Teichmüller spaces of Riemann surfaces

Thomas Gauglhofer

Using an algebraic formalism based on matrices in SL(2,R), we explicitly give the Teichmüller spaces of Riemann surfaces of signature (0,4) (X pieces), (1,2) ("Fish" pieces) and (2,0) in trace coordinates. The approach, based upon gluing together two build ...

EPFL2006

Trace coordinates of Teichmüller space of Riemann surfaces of signature $(0,4)$

Klaus-Dieter Semmler, Thomas Gauglhofer

Summary: We explicitly give

calT

, the Teichmüller space of four-holed spheres (which we call

X

pieces) in trace coordinates, as well as its modular group and a fundamental domain for the action of this group on

calT

which is its moduli space. As a co ...

2005